A geometric view on local Lorentz transformations in teleparallel gravity

Local Lorentz transformations play an important role in teleparallel gravity theories, which a tetrad is conventionally employed as fundamental field variable describing the gravitational field. It commonly understood that modifications of general relativity framework break certain notion local invariance, present pure formulation such while another covariant preserved. We illuminate these different notions from geometric perspective, and distinguish them what breaking invariance context phenomenology. Based on physical arguments, we interpretation dynamical fields gravity, unifies refines conventional approaches.